Scalable Monte Carlo inference for state-space models

TL;DR

This paper introduces a new simulation-based likelihood ratio estimation method for state-space models using conditional Sequential Monte Carlo, improving variance reduction and scalability in Bayesian inference with large datasets.

Contribution

The paper proposes a novel likelihood ratio estimator leveraging cSMC, leading to scalable, variance-reducing MCMC algorithms for Bayesian inference in state-space models.

Findings

Variance of estimator decreases as likelihood parameters get closer.

New MCMC methods scale efficiently with large datasets.

Simulation results show improved computational efficiency over existing methods.

Abstract

We present an original simulation-based method to estimate likelihood ratios efficiently for general state-space models. Our method relies on a novel use of the conditional Sequential Monte Carlo (cSMC) algorithm introduced in \citet{Andrieu_et_al_2010} and presents several practical advantages over standard approaches. The ratio is estimated using a unique source of randomness instead of estimating separately the two likelihood terms involved. Beyond the benefits in terms of variance reduction one may expect in general from this type of approach, an important point here is that the variance of this estimator decreases as the distance between the likelihood parameters decreases. We show how this can be exploited in the context of Monte Carlo Markov chain (MCMC) algorithms, leading to the development of a new class of exact-approximate MCMC methods to perform Bayesian static parameter inference in state-space models. We show through simulations that, in contrast to the Particle Marginal Metropolis-Hastings (PMMH) algorithm of Andrieu_et_al_2010, the computational effort required by this novel MCMC scheme scales very favourably for large data sets.